Copyright © 2009 J.-M. Barbaroux and J.-C. Guillot. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider a Hamiltonian with cutoffs describing the weak decay
of spin 1 massive bosons into the full family of leptons. The Hamiltonian is
a self-adjoint operator in an appropriate Fock space with a unique ground
state. We prove a Mourre estimate and a limiting absorption principle above
the ground state energy and below the first threshold for a sufficiently small
coupling constant. As a corollary, we prove the absence of eigenvalues and absolute
continuity of the energy spectrum in the same spectral interval.